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N. Osmolovskii, V.M. Veliov:
"On the Strong Metric Subregularity in Mathematical Programming";
Research Reports (Vienna University of Technology, Institute of Statistics and Mathematical Methods in Economics, Operations Research and Control Systems), 2020-09 (2020), 09; 15 S.

This note presents sufficient conditions for the property of strong metric subregularity(SMSr) of the system of first order optimality conditions for a mathematical programmingproblem in a Banach space (the Karush-Kuhn-Tucker conditions). The constraints of theproblem consist of equations in a Banach space setting and finite number of inequalities.The conditions under which SMSr is proved involve Fr ́echet differentiability of the data,strict Mangasarian-Fromovitz constraint qualification, and second-order sufficient optimal-ity condition. The obtained result extends the one known for finite-dimensional problems.Although the applicability of the result is limited in the truly Banach space setting (due tothe Fr ́echet differentiability assumptions and the finite number of inequality constraints), thepaper can be valuable due the self-contained exposition, and provides a ground for extensionsthat are applicable in calculus of variations and optimal control.

optimization, mathematical programming, Karush-Kuhn-Tucker conditions, metric regularity

https://publik.tuwien.ac.at/files/publik_289721.pdf